DeSitter and AntiDeSitter Universe

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If the DeSitter Universe is modeled by Empty Universe
1. Very Early Universe with Inflaton Field
2. Very Far Universe in Future when Black Holes have evaporated

 

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Q1
What Einstein model currently describes a Homogeneous and Isotropic approximated Universe with Matter with positive Lambda, is it still Friedmann (FLRW) or have models moved on

Which Einstein model describes an Inhomogeneous and Anisotropic very early universe with primordial density fluctuations

 

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Q2

Are there any scenarios for an AntiDeSitter Model in the chronology of the Universe

 

[Mordred]

Q1
What Einstein model currently describes a Homogeneous and Isotropic approximated Universe with Matter with positive Lambda, is it still Friedmann (FLRW) or have models moved on

Which Einstein model describes an Inhomogeneous and Anisotropic very early universe with primordial density fluctuations

Its still the FLRW metric or more specifically the LCDM model, \LambdaCDM. Which also involves the Eintein field equations..
as far as the De-sitter universe usages you will probably be interested in this article.

De-Sitter musings

http://arxiv.org/abs/1205.3855

also a string theory model variant uses ADS.
ADS/CFT Anti-Desitter correspondance I'm not too familiar with how this model works yet to supply any details.

 

[Quantizer]

Its still the FLRW metric or more specifically the LCDM model, \LambdaCDM. Which also involves the Eintein field equations..
as far as the De-sitter universe usages you will probably be interested in this article.

De-Sitter musings

http://arxiv.org/abs/1205.3855

also a string theory model variant uses ADS.
ADS/CFT Anti-Desitter correspondance I'm not too familiar with how this model works yet to supply any details.

Thanks for that Mordred, a few pages in and already intrigued by some of the astronomical exponentials being put forward